Inspired by a question yesterday, I thought I'd try my hand at a LaTeX3 solution which would show how to convert base 10 numbers into any other base of the user's choice.

Yesterday I wrote a nice simple version that worked. But today, I decided I wanted to separate the building of the steps from the process of outputting and formatting those steps. I also thought it would be interesting to explore the possibilities of creating the effect of an array within an array using sequences and token lists.

# must be doubled, so I guess you need ####1.
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egregFeb 2 '13 at 16:30

@egreg. That works. Thanks. But it also seem peculiar and counter-intuitive to how LaTeX usually works. Why the need for the doubling?
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A.EllettFeb 2 '13 at 16:32

Not related to the issue at hand, but expl3 code should always be set up in a defined namespace. So here you might have \showbaseconv_... as the function prefix, and therefore \l_showbaseconv_... for a local variable, etc.
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Joseph Wright♦Feb 2 '13 at 16:33

@A.Ellett No, it's entirely how TeX works: each time you nest a level of definitions, you have to double up each #.
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Joseph Wright♦Feb 2 '13 at 16:33